Impulse Control of a Diffusion with a Change Point

Abstract: This paper solves a Bayes sequential impulse control problem for a diffusion, whose drift has an unobservable parameter with a change point. The partially-observed problem is reformulated into one with full observations, via a change of probability measure which removes the drift. The optimal impulse controls can be expressed in terms of the solutions and the current values of a Markov process adapted to the observation filtration. We shall illustrate the application of our results using the Longstaff-Schwartz algorithm for multiple optimal stopping times in a geometric Brownian motion stock price model with drift uncertainty.